Question

4. For the game below,

a. Find all values of x and y such that it is a Prisoner’s Dilemma. b. Find all values for x and y such that it is a coordination game.

		Barbara	Barbara
		Alpha	Beta
Kenneth	Alpha	8,8	Y,X
Kenneth	Beta	X,Y	3,3

Barbara Alpha Beta Kenneth Alpha 8, 8 Y, X Beta X, Y 3, 3

Answer 1

a. values of x and y such that it is a Prisoner’s Dilemma:
X = any number greater than 8;
Y = any number less than 3.

b. values for x and y such that it is a coordination game:
X = any number less than 8;
Y = any number less than 3.

As illustration, here are examples of each type of game:

Prisoners dilemma:

Prisoners dilemma is a game where players settle for the second best response. Here Barbara and Kenneth play (Beta, Beta) although (Alpha, Alpha) would fetch them higher payoffs.

Coordination game:

Coordination game is where both players choose the same strategy (Battle of sexes is a common example). In the game above, both choose Alpha or both choose Beta as their best response.